I have read and heard a lot of hype about Mathematica 4.0
"featuring a
New Generation of
Fast Numerics"
e.g. on www.wri.com .
However, in the real world it is hard to find anything to get excited about.
I have had several disappointing results from 4.0, here are the latest:
On a P450/NT I ran a very simple Crank-Nicholson integration of a
one-dimensional quantum free-particle wave-packet with x-dimensioned to 1001
points and time to 401 points - no error checks or adaptive stepsize, just
plug-and-chug. Runtime under 4.0 was 501 seconds, 3.0 was 480 seconds, but
who's quibbling; however, in FORTRAN this ran in 8 seconds. I don't even
consider this to be "fast numerics", but 501 seconds sure isn't. I would
like to know where all this speed is so I can use some of it, or am I
missing something?
When I ran the FORTRAN code and then read it into Mathematica, it still was faster
than the Mathematica code alone, although the ReadList I used on the ASCII
file did take some time. When I upped the dimensions to 2001 x 1001, the
FORTRAN ran in about 40 s - most of this is for the output; however, when I
tried to read it in to Mathematica, it took forever, and on the subsequent plot it
bombed the Kernel. I then made the mistake of saving the NB which managed
to acquire an error so that I can't open it anymore - 6 Mb of useless NB!
--
Kevin J. McCann
Johns Hopkins University APL